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sympy__sympy-18199

Based on my analysis of the issue and the existing patch example, I can generate the proper patch. The issue is that nthroot_mod doesn't check for the case where a % p == 0, which means x = 0 should be a valid root.

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Install (Claude Code)

mkdir -p .claude/skills/sympy-sympy-18199-2 && curl -fsSL https://doutorai.pt/data/lib/skills__sympy-sympy-18199-2.md -o .claude/skills/sympy-sympy-18199-2/SKILL.md

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Content

# sympy__sympy-18199
# Loki Mode Multi-Agent Patch
# Attempts: 1

Based on my analysis of the issue and the existing patch example, I can generate the proper patch. The issue is that `nthroot_mod` doesn't check for the case where `a % p == 0`, which means `x = 0` should be a valid root.

```
--- a/sympy/ntheory/residue_ntheory.py
+++ b/sympy/ntheory/residue_ntheory.py
@@ -746,6 +746,14 @@ def nthroot_mod(a, n, p, all_roots=False):
     a, n, p = as_int(a), as_int(n), as_int(p)
     if n < 1:
         raise ValueError("n should be positive")
+
+    # If a % p == 0, then x = 0 is a root since 0*

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